The increasing quality of digital transmission technology is placing greater demands on the requirements for digital filters. In particular, the requirements for stop band attenuation and the width of the transition region are becoming more challenging to meet. For example, in typical audio applications, filters with 100 dB stop band attenuation, and a transition region spanning 0.5 kHz or less are desired. Additionally, requirements that such filters operate at high speed, low power, and be as inexpensive as possible make digital filters that use as few operations as possible increasingly desirable. For these and other reasons, there is a need for the present invention as set forth in the following embodiments.